T HE Latitude of a Place, is the Distance of the Equator from the Parallel of that Place, reckoned in the Degrees of the Brass Meridian; and is either Northor South, according as it lyes between the North or South Poles of the Equator. To find the Latitude, bring the Mark of the Place, suppose London, to be the Brazen Meridian; then count the Number of Degrees upon the Meridian, contained between the Equator and the Place. Thus you shall find the Latitude, by this new Globe, of London, to be 51 Deg. 30 Min. and of Two Places, which differ only in Latitude, to find their Distance. I N this there are Two Varieties of Position. 1. If both the Places lye under the fame Meridian, and on one and the fame Side of the Æquinoctial: Substract the Leffer Latitude from the Greater, the Difference (or Remainder) reduced into Miles, (by allowing 60 Deg. to One Mile) shall give you the Distance. Exam Example. London and Ribadio lye both under the fame Me- Fig. ridian, but differ in Latitude: For London hath 51 Deg. 30 Min. XXVI. of Latitude, at L, and Ribadio hath 34 Deg. of Latitude, at R, both North; the Difference of Latitude is 17 Deg. 30 Min. equal to the Arch LR: And that Reduced into Miles, makes 1050 for their Distance. 2. If the Two Places lye under the same Meridian, but in different Hemispheres, i. e. one on the North, and the other on the South Side of the Equinoctial: Then, Add both the Latitudes together, and the Sum of them is their Distance.. Example. London, and the Island Tristan Dacunhu, lye both under One Meridian, but London hath 51 Deg. 30 Min. of North Latitude, at L, and the Island hath 34 Deg. of South Latitude, at D; the Sum of these Two Latitudes is 85 Deg. 30 Min. equal to the Arch of the Meridian LED; the which reduced into Miles, (by multiplying the Degrees by 60, and allowing for every Minute One Mile) makes 5130 Miles, for their Distance. PROB. IV. Two Places, which differ in Longitude only; To find their Distance. N this there are Two Varieties of Pofition. IN : 1. If the Two Places lye both under the Equinoctial, and have no Latitude; in this Case, Their Difference of Longitude (if it be less than 180 Deg.) is their Distance: But, if the Difference exceed 180 Deg. Subtract it from 360 Deg. and the Remainder is their Distance, in Degrees. Example. The Island Samatra, and Island St. Thomas, lye both under the Aquinoctial: St. Thomas having 22 Deg. 10 Min. of Longitude at T, and the Island Sumatra 82 Deg. 10 Min. at S. Now, the Leffer Longitude 22 Deg. 10 Min. substracted from the Greater 82 Deg. 10 Min. leaves 60 Deg. equal to the Arch S T, for their Difference in Degrees: Which converted into Miles, makes 3600, and fo many Miles are the Two Islands distant from each other. 2. But if the Two Places differ only in Longitude, and lye not in the Equinoctial, but under some other intermediate Parallel of Latitude: As Hierufalem at H, and Baldo at B; both in the Parallel of 31 Deg. 40 Min. of North Latitude, but differing in Longitude 60 D. g. 15 Min. equal to the Angle HPB, to find the Distance of these Two Places. Fig. XXVI. I. By the Globe. Apply the Quadrant of Altitude, or Brass Plate, to the Two Places, and the Number of Degrees thereof contained between the Two Places, is their Distance, which will be found to be 50 Deg. 32 Min. II. By Trigonometrical Calculation.. The Quadrant of Altitude (or Brass Plate) applied to the Two Places, is represented by the Arch HB, and the Arches of the Two Meridians, which pass through the Two Places, are PBN and PHM; and PB and PH, are equal to the Complement of of the Latitude of both the Places, viz. 58 Deg. 20 Min. So that now you have constituted upon the Globe an Oblique Spherical Triangle PBH; in which you have given, (1.) The Two Sides PB and PH, both equal to 58 Deg. 20 Min. the Complement of the Latitude. (2.) The Angle BPH 60 Deg.. 15 Min. the. Difference of the Longitude of the Two given Places. To find the Side B H, their Distance. For which this is The Canon for Calculation. By CASE I. of R. A. S. T. Is to the Co-fine of the Common Latitude (PHorPB) 58 D. 20M.. To to Sine of half the Distance (half BH) 25 Deg. 16 Min. The Double whereof, 50 Deg. 32 Min. is the Distance BH, which in Miles is 3032 Miles. PROB. V. Two Places, which differ both in Longitude and Latitude; to find their Distance. I N this there are Three various Positions. 1. If one of the Places lye under the Equinoctial, and fo have. no Latitude; and the other under some Parallel of Latitude be: tween the Equinoctial, and one of the Poles: As London, in 51 Deg. 30 Min. of North Latitude at L; and St. Thomas Illand: under the Æquinoctial at T, but differ in Longitude 18. Deg. For finding the Distance of these Two Places. I. Ufon I. Upon the Terrestrial Globe. Fig. Bring London to the Brass Meridian, and over it, fix the Qua XXVI. drant of Altitude: The Globe being in this Position, bring the Quadrant of Altitude to lye just over St. Thomas Island, and you will find it cut the Quadrant of Altitude, in 54 Deg. 45 Min. for the Distance of the Two Places. II. By Trigonometrical Calculation. The Globe resting in the former Position, you will find conftituted upon it a Right-angled Spherical Triangle LÆT, composed of, (1.) LE, an Arch of the Brass Meridian. (2.) ET, an Arch of the Equinoctial. And, (3.) LT, an Arch of a Great Circle (made by the Quadrant of Altitude) paffing through both the Places: And in this Triangle, you have given, (befides the Right Angle at E) (1.) The Perpendicular LE, the Latitude of London, 51 Deg. 30 Min. (2.) The Angle at L, the Difference of Longitude 18 Deg. 10 Min. To find the Hypotenuse LT, the Distance. The Canon for Calculation. By CASE XIV. of R. A. S. T. As Tang. of the Latitude L Æ, 51 Deg. 30 Min. Is to the Radius; So is the Co-fine of ALT, 18 Deg. 10 Min. 2. If both the Places proposed shall be without the Æquinoctial, but both of them, either on the North of South Side thereof: As London in 31 Deg. 30 Min. at L, and Hierufalem in 31 Deg. 40 Min. at H, both on the North Side of the Equinoctial; and their Difference of Longitude 46 Deg: To find their Distance Upon the Terrestrial Globe. Bring one of the Places, as London, to the Brass Meridian, and over it screw the Quadrant of Altitude, and keep the Globe there fixed, then move the Quadrant of Altitude, till it lye over HieruSalem, and you shall find it to lye under 39 Deg. 32 Min. of the Quadrant: And that is the Distance of the Two Places. Fig. XXVI. By Trigonometrical Calculation. The Globe being in the former Position, you will find upon it an Oblique-angled Spherical Triangle, composed of PL, an Arch of the Brass Meridian: Of PH, an Arch of the Meridian that paf seth over Hierufalem; and of L H, an Arch of the Quadrant of Altitude. In which Triangle you have given, (1.) PL, the Com plement of the Latitude of London, 38 Deg. 30 Min. (2.) The Side PH (the Complement of the Latitude of Hierufalem 59 Deg. 20 Min. (3.) The Angle LPH, the Difference of Longi tude of the Two Places, 46 Deg. To find the Two Angles of Pofition at Land H: And, (2.) The Side LH, the Distance of the Two Places. The Canons for Calculation. By CASE III. and CASE IX. of A.O. S. T.. (1.) As the Sine of half the Sum of the Sides PL and PH, 48 Deg. 25 Min. Is to the Sine of half their Difference, 9 Dég. 55 Min. So is the Co-tangent of half the Difference of Longitude (i. e.) half the Angle LPH, 23 Deg. To the Tangent of 28 Deg. 29 Min. Which is the half Difference of the Angles PLH and PHL. (2.) As the Co-fine of half the Sum of the Sides PLand. PH, 41 Deg. 35 Min. Is to the Co-fine of half their Difference, 80 Deg. 2 Min. half the Angle LPH 23 Deg. To the Tangent of 74 Deg. 2 Min. Which is the Tangent of half the Sum of the Two Angles The |